Orderings of a class of trees with respect to the Merrifield–Simmons index and the Hosoya index

The Merrifield–Simmons index and the Hosoya index are two prominent molecular graph descriptors in mathematical chemistry. The Merrifield–Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, the Merrifield–Simmons index and the Hosoya index of a class of trees Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \Gamma $$\end{document} are investigated, and their orderings and extremal trees with respect to these two topological indices are obtained, respectively.